In the previous post, we have learned a strategy on multiplying whole numbers by mixed fractions. We have learned that instead of converting the mixed fraction part to improper fractions, we split the numbers and the fraction and then multiplied them separately.
One example for this is 8 ¾ × 2. Instead of converting 8 ¾ to the improper fraction 35/4, we then split it to 8 and ¾ and then multiply each by 2. Therefore, 8 × 2 = 16 and ¾ × 2 = 3/2 which means equals to 17 ½.
Now, why does this math trick work?
First we know that 8 ¾ really means 8 and ¾ which is equal to 8 + ¾. Now, if we multiply 8 + ¾ by 2, we have
2(8 + ¾) = 2(8) + 2(¾) = 16 + 6/4 = 16 + 3/2.
Are the expressions and equations familiar?
The Whole Number Mixed Fraction Multiplication Secret
Yes they are. If you have already discussed the distributive property of multiplication over addition in your class, then you are familiar with the equation
a(b + c) = ab + ac
where a, b, and c are real numbers.
In the expression above, a = 2, b = 8 and c = ¾.
And as mentioned above, the distributive property works for all real numbers, so it will work with 3/4 since 3/4 is a real number.
That’s it. At least now, you know why the math trick works.
Remember, it’s cool to know the trick. But it’s even cooler if you know why the trick works.